Horner versus Holdred: An Episode in the History of Root Computation

Abstract

It is well known that Horner's method for the computation of a real root of a polynomial equation was anticipated in Italy by Ruffini. In the present paper it is shown that in England the method was published by Holdred, before Horner. The resulting controversy over priority is discussed, and related letters from contemporary mathematicians are reproduced. It is concluded that the dissemination of the algorithm under the inappropriate designation "Horner's method" is mainly due to De Morgan. C 1999 Academic Press Il est bien connu que la méthode de Horner pour calculer une racine reélle d'uneéquation polynôme avaitété anticipée en Italie par Ruffini. Dans ce papier il est démontré qu'en Angleterre la méthode fut publiée par Holdred avant Horner. La controverse sur la priorité est discutée, et des lettres de mathématiciens contemporains sont reproduites. Il est conclu que la dissémination de l'algorithme sous la désignation inappropriée "méthode de Horner" est principalement dueà De Morgan. C 1999 Academic Press MSC 1991 subject classifications: 01A55; 01A70; 01A80; 65-03. mentioned above, gives in his Theory of Equations (1867) a clear account of the basic method of root computation [72,[150][151][152][153][154][155][156][157][158][159][160][161][162][163][164]. But he ascribed this to Horner, referring to De Morgan [22] for the history.

On the Square Root Computation in Liber Abaci and De Practica Geometrie by Fibonacci

“…Fibonacci's method to compute the integer part of the square root is in a wider class of digit-by-digit methods. Contrary to methods often called evolution methods [20,21] which evolve one digit at the time, Fibonacci's method is a (front-end) recursion. In Hughes' translation of De Practica Geometrie [10] (p. 36), he demonstrates Fibonacci's square root computation of √ 864 in seven steps all based on the binomial expansion (1).…”